Optimal time-decay estimates for the compressible Navier-Stokes equations in the critical $L^p$ framework
The global existence issue for the isentropic compressible Navier-Stokes equations in the critical regularity framework has been addressed by R. Danchin more than fifteen years ago. However, whether (optimal) time-decay rates could be shown in general critical spaces and any dimension $d\geq2$ has remained an open question. Here we give a positive answer in more general $L^p$ critical framework. This is a joint work with R. Danchin.